The very fact you've used your private key to send money to the small wallet means that private key is no longer safe?
This is the part that I don't really understand yet either
Well no... it doesn't necessarily mean that. Like the one poster said, its as safe as putting your credit card info through the internet tubes. But if that gets intercepted you have recourse.
If you're confident that you don't have any malware, either because you use linux, or because you're a total geek, or if you're not buying too awfully damn much bitcoin then you're PROBABLY ok just using a regular old bitcoin wallet client from bitcoin.org.
But when you're holding enough to effect your life, you'll probably wanna take more paranoid precautions like the ones described, at least until this is mass-friendly.
No, bitcoin is much safer than sending credit card information. If somebody intercepts your credit card information then they can go use your credit card information anywhere they want. If somebody intercepts your bitcoins transaction message, they can do nothing because it does not include the private key, just a message signed by the private key. They could not generate any other spends because they do not have the key.